A certain sum amounts to Rs 2584 at 15% per annum simple interest in \(2\frac{2}{5}\) years. What is double the sum?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs 3800
Under simple interest, the amount = principal + interest, and the interest for \(T\) years at \(R\%\) is \(\frac{RT}{100}\) of the principal.
Time \(\displaystyle =2\frac{2}{5}=\frac{12}{5}\) years, rate \(=15\%\)
Interest \(\displaystyle =\frac{15\times12}{5\times100}=\frac{36}{100}\) of the sum, i.e. 36% of the sum
Amount \(=136\%\) of the sum \(=\) Rs 2584
Sum \(\displaystyle =\frac{2584\times100}{136}=\) Rs 1900
Double the sum \(=2\times1900=\) Rs 3800
Double the sum is Rs 3800. (Rs 1900, Option (1), is the sum itself.)